Checkerboard Artifacts when Sculpting
This is just a half-answer.
Causes
As I looked closely into the difference of your meshes ...


Some of the wrinkle in your sculpting is more in the diagonal direction of the edge than the tutorial.

Your brush seem to adjust only in Normal direction of the mesh, but tutorial brush seems to also pull nearby vertices close together to keep up with the deep detail.


Workarounds
There are 2 different approaches I can think of.

This one is more of the macro level.      I googled and found 2 links. (https://www.youtube.com/watch?v=vYzS94fPo1w, and https://www.youtube.com/watch?v=MLUnfE4FcOY)
They use cloth simulation to (automatically) generate wrinkle and pull vertices to the location that needed.    Thus the artifact become less.

However, I believe the main problem is the sculpting brush type.
The correct brushes should have pinch attribute e.g. pinch-brush itself (but has no add/subtract mode, sadly), or crease-brush.
The pinch (search for the word in https://docs.blender.org/manual/en/2.82/sculpt_paint/sculpting/tools.html) means to will pull vertices together when sculpting.
If there are enough vertices, just the crease-brush should be enough. (as I found in https://www.youtube.com/watch?v=vbUJVzBBlVY )


Here is the setting of crease-brush. Not every brush type has this pinch feature.

Here is my attempt to reduce the artifact.  I used pinch-brush after normal sculpting.    After the process, it is noticeable that the result become better.  I didn't use crease-brush though.